Yep. DD1 did this when she left for Uni. She phoned my niece after we left her at halls and was giving her the full trembly lip treatment and saying that she missed us. My niece then told my sister, who then phoned me to tell me

I tried to contact DD to see if she was OK, but no reply (poor mobile signal). She called the next day and was full of how wonderful everything was - the previous evening she would have been too busy making friends with her flat mates to take my call. I, however, had spent a sleepless night, worried that she would be unhappy.

Your DD will be fine, I'm sure. She is doing something that she loves and gaining a little bit of independence at the same time. It will look great on her CV too.